Can i run a standalone game at a resolution of the NES?

I want to make an 8-bit like game, with the small resolution, but how do you make a resolution like 320x480 work in a standalone game?

Well, there are two ways to handle this, really.

You can either force a fixed-resolution for the game through the Standalone Player Settings or you can fix the final render resolution using a Render Texture and (optional) full-screen shader. As an example of the latter solution:

// Simple example in C#
// This script should be attached to the main camera
// Uses fixed width of "baseWidth" with square pixels matching aspect ratio
public int baseWidth = 480;
RenderTexture rt;

void Start()
{
	int aspectHeight = Mathf.CeilToInt(baseWidth * ((float)Screen.height / Screen.width));
	rt = new RenderTexture(baseWidth, aspectHeight, 0);
	rt.filterMode = FilterMode.Point;
}

void OnRenderImage(RenderTexture source, RenderTexture destination)
{
	Graphics.Blit(source, rt);
	Graphics.Blit(rt, destination);
}

Edit: As a further example of a way to perform the initial render at that reduced resolution (rather than scaling down a full-resolution render):
public int baseWidth = 480;
Rect baseRect;
Rect scaledRect;
RenderTexture rt;
Camera cam;

void Start()
{
	int aspectHeight = Mathf.CeilToInt(baseWidth * ((float)Screen.height / Screen.width));
	cam = GetComponent<Camera>();
	baseRect = cam.rect;
	scaledRect = new Rect(baseRect.x, baseRect.y, (float)baseWidth / Screen.width, (float)aspectHeight / Screen.height);
}

void OnPreRender()
{
	cam.rect = scaledRect;
}

void OnRenderImage(RenderTexture source, RenderTexture destination)
{
	cam.rect = baseRect;
	Graphics.Blit(source, destination);
}